FIBONACCI SUMMATION ECONOMICS PART I I *
Albert J. Faulconbridge
Chicago, I l l i n o i s
E l l i o t ' s o b s e r v a t i o n s have a l e r t e d us to the possible e x i s t e n c e
of untouched fields
of Fibonacci s u m m a t i o n p r i n c i p l e s r e l a t i n g to
economic prediction*
Dependence upon coincidence
u n r e l a t e d facts invites e r r o r .
and
seemingly
An a t t e m p t to induce o r d e r l i n e s s into
the investigation will be m a d e ,
When r e a s o n i n g has gone a s far a s
p o s s i b l e at the m o m e n t a working model c o n s i s t e n t with the p r o d u c t s
of the fledgling r e a s o n i n g will be c o n s t r u c t e d which model,
if it works.,
p r o v i d e s some evidence that the r e a s o n i n g might not be sufficiently
e r r o n e o u s to discard*
To induce this o r d e r l i n e s s p a r a l l e l topics will
be developed to a d e g r e e such that they can l a t e r be fused to purpose„
These topics a r e :
1.
What cycles have been o b s e r v e d ?
2.
What r e l a t i o n s h i p s ,
3.
What other a p p a r e n t c o - i n c i d e n c e s exist that might be
if any, do t h e s e c y c l e s have to the
Fibonacci s e q u e n c e s ?
r e l a t e d to the p r o b l e m ?
1.
W H A T CYCLES HAVE BEEN OBSERVED?
The s o u r c e for t h e s e c y c l e s is r e l a t i v e l y incomplete for at the
t i m e this a r t i c l e will a p p e a r in p r i n t t h e r e will have been published a
complete compendium of cycles identified to date by the Foundation for
the Study of Cycles,,
P a r t i a l l y completed data shows a list of c y c l e s
in m a n y phenomena which on s u p e r f i c i a l examination b e a r s no r e l a t i o n
to Fibonacci s e r i e s but when a r r a n g e d into subgroups c o n s i s t e n t within t h e m s e l v e s do in fact show some tendency toward s u m m a t i o n r e lationships.
Some l a r g e r cycle groups show two or m o r e s u m m a t i o n
r e l a t i o n s h i p s but with different time periods*
Notably t h e r e a r e 17y week cycles in i n d u s t r i a l stocks and e l e c t r i c a l potential of t r e e s ,
5.9,
12 and 13 month c y c l e s in i n d u s t r i a l
stocks; a 1Z month or 1 3 lunar month cycle in m a n y phenomena including
industrial stocks,
some c o m m o d i t y p r i c e s ,
r a t i o of m a l e to female
Refer to P a r t I, Fibonacci Q u a r t e r l y , D e c e m b e r 1964, page 320.
309
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FIBONACCI SUMMATION ECONOMICS P A R T II
conceptions,
sleep c h a r a c t e r i s t i c s ,
d o m e s t i c fowl,
Dec.
beef cattle p r i c e s , egg laying of
incidence of p u e r p e r a l s e p s i s ; a 17 0 8 month cycle in
i n d u s t r i a l s t o c k p r i c e s , a 21 month cycle in rainfall in the G r e a t Lakes
region; a two y e a r cycle in i n d u s t r i a l stock p r i c e s , G r e a t Lakes r a i n fall,
sunspot n u m b e r s and Nile R i v e r floods; a grouping around 34
lunar months of such c y c l e s a s r e s i d e n t i a l c o n s t r u c t i o n
contracts,
copper commodity p r i c e s , pig i r o n p r i c e s , automobile factory s a l e s ,
Canadian Pacific Railway r e v e n u e t o n - m i l e s ,
G r e a t Lakes rainfall,
rayon production, some individual company s a l e s , m o t o r c a r and t r u c k
sales,
d e p a r t m e n t s t o r e s a l e s and copper company s h a r e p r i c e s ; a 3
y e a r cycle in factory s a l e s of p a s s e n g e r c a r s ; a 3,2 to 3. 4 y e a r g r o u p ing in stock p r i c e s ,
bank c l e a r i n g s ,
copper s h a r e p r i c e s ,
b u s i n e s s conditions, pig i r o n production,
general
f a c t o r y s a l e s of c a r s , a t -
m o s p h e r i c e l e c t r i c i t y , b u s i n e s s f a i l u r e s , cocoa bean p r i c e s , and the
s o l a r constant; t h e r e is a 4. 2 to 4. 4 y e a r or roughly a 55 lunar month
cycle in company s a l e s , t e m p e r a t u r e , i n d u s t r i a l c o m m o n stock, r a i l road stock p r i c e s , a d v e r t i s i n g effectiveness, E u r o p e a n wheat p r i c e s ,
pig i r o n p r i c e s and G r e a t Lakes rainfall.
There is an i m p r e s s i v e group of cycles c l u s t e r e d within the 5. 90
to 5. 96 y e a r p e r i o d including the one fifth s i d e r e a l p e r i o d of Saturn,
liabilities of b u s i n e s s f a i l u r e s , r a i l r o a d stock p r i c e s , sunspots with
a l t e r n a t e cycles r e v e r s e d , s u n s p o t s , the combined index of s t o c k p r i c e s ,
copper, cottonand pig i r o n p r i c e s , coal s t o c k s , t r e e ring s i z e , wheat
p r i c e s and b a r o m e t r i c p r e s s u r e .
T h e r e is an 8 y e a r cycle in cotton p r i c e s , c i g a r e t t e production,
lynx abundance, pig i r o n p r i c e s , r a i l stock p r i c e s , c r o p y i e l d s , bird
abundance, i n d u s t r i a l s a l e s ,
rainfall,
wholesale p r i c e index,
steel
ingot production, sunspots with a l t e r n a t e c y c l e s r e v e r s e d , wheat p r i c e s ,
an 8. 8 to 9. 6 y e a r cycle in s u n s p o t s , widths of p r e - g l a c i a l t r e e r i n g s ,
pig i r o n p r i c e s , n u m b e r s of cattle r a i s e d , wholesale c o m m o d i t y p r i c e s ,
v a r i o u s stock p r i c e c a t e g o r i e s , g r a s s h o p p e r abundance, auto p r o d u c tion,
B r i t i s h Consol p r i c e s ,
b u s i n e s s activity,
copper p r i c e s ,
in-
d u s t r i a l , r a i l r o a d and combined s t o c k p r i c e s , liabilities of c o m m e r c i a l
and financial f a i l u r e s ,
Protestant churches,
manufacturing production,
new m e m b e r s of
pig i r o n p r i c e s , manufacturing s a l e s , c u r r e n t
1965
FIBONACCI SUMMATION ECONOMICS P A R T II
311
t r e e ring widths, wool p r i c e s , b u s i n e s s f a i l u r e s , patents i s s u e d , cott o n p r i c e s , abundance of m a r t e n , r a b b i t s , lynx, foxes, t i c k s , wolves,
a c r e a g e planted to wheat, Atlantic s a l m o n and other fish abundance,
h u m a n h e a r t d i s e a s e incidence, India rainfall, lunar cycle, ozone at
London and P a r i s and tent c a t e p i l l a r s ; an 1 1 , 4 to 11.8 y e a r cycle in
rainfall,
twin and genius b i r t h s , infectious d i s e a s e incidence,
sex
r a t i o of m a l e to female b i r t h s , s l e n d e r n e s s of newborn, s u n s p o t s , and
in the n u m b e r of i n t e r n a t i o n a l b a t t l e s ,
T h e r e is an i m m e n s e group of c y c l e s whose p e r i o d s lie between
17. 0 and 18. 3 y e a r s and some of whose exact Length has been worked
out a c c u r a t e to two d e c i m a l p l a c e s .
This group includes the Smith-
sonian s o l a r constant, rainfall f i g u r e s , cattle p r i c e s , m e a n t e m p e r a t u r e s , building c o n s t r u c t i o n , r e a l e s t a t e activity, population, c o m m o n
stock p r i c e s , wheat p r i c e s , sunspot n u m b e r s r e v e r s e d , Nile floods,
earthquakes,
pig i r o n p r i c e s , cycle in the v a r i a b l e s t a r Scorpius V,
in war incidence, A r i z o n a t r e e ring, b u s i n e s s f a i l u r e s , cotton p r i c e s ,
i n t e r n a t i o n a l b a t t l e s , and in civil w a r , sunspots with a l t e r n a t e cycles
reversed,
tree rings,
a d v a n c e s and r e c e s s i o n s of g l a c i e r s , i m m i g r a t i o n ,
s a l e s of a public utility company,
Java
c o m m o n stock lows,
Canadian Pacific R a i l r o a d freight traffic, furniture production, loans
and d i s c o u n t s , l u m b e r production, financial p a n i c s , pig i r o n p r o d u c tion, m a r r i a g e s , sunspots with a l t e r n a t e cycles r e v e r s e d , and wheat
acreage inverted.
T h e r e is a 34 to 36 y e a r grouping which includes cycles in E-urop e a n h a r v e s t s , U . S . A . I m m i g r a t i o n , plant and t r e e growth i n E u r o p e ,
E u r o p e a n t r e e ring t h i c k n e s s , lynx abundance, e a r t h q u a k e s in China,
E u r o p e a n w e a t h e r , frequency of the A u r o r a B o r e a l i s , E u r o p e a n b a r o metric pressure,
m a n u f a c t u r i n g production of the U. S» A. , p r i c e s of
B r i t i s h Consols, and E u r o p e a n wheat p r i c e s .
A 42 y e a r cycle e x i s t s in a g r i c u l t u r e and r e l a t e d phenomena including t r e e ring widths, cotton p r i c e s , wheat p r i c e s , and s u n s p o t s .
A 55 y e a r cycle e x i s t s in i n d u s t r i a l and r e l a t e d phenomena including G e r m a n coal production,
v a r i o u s English, F r e n c h and U. S.
i n d u s t r i a l s t a t i s t i c s , worldwide pig i r o n and coal production and r a i l road stock p r i c e s .
T h e r e is a l s o some reflection in E u r o p e a n wheat
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FIBONACCI SUMMATION ECONOMICS PART II
p r i c e s and t r e e ring widths.
Dec.
FinaLly t h e r e is a 67 and 144 y e a r cycle
in i n t e r n a t i o n a l b a t t l e s .
When individual phenomena a r e investigated a n u m b e r of cycles
have a l r e a d y been identified.
R a i l r o a d s t o c k p r i c e s show cycles of 4. 4,
5 . 9 , 5.92, 6.4, 7 . 9 5 , 8. 39, and t h r e e cycles of 9. 18, 9. 20, and 9. 30
y e a r s , 18-^5.91,
y e a r s and 55 y e a r s .
6 . 3 to 6 . 5 ,
8,
8.9,
Pig i r o n p r i c e s show 2 . 7 ,
9o 0, to 9 . 3 ,
Copper commodity p r i c e s show 2 . 7 ,
9.2,
17.69,
4.4,
17.75 y e a r s .
5 . 9 1 , 9.0 to 9 . 3 y e a r c y c l e s .
Coal production and coal stocks show 5 . 9 1 , 8.0, 17.75 and 55 y e a r
cycles.
Sunspot n u m b e r s with a l t e r n a t e cycles r e v e r s e d show 5. 9,
5. 91, 8, 17, 17. 3, 17. 66, 17. 75, 18. 33 y e a r c y c l e s .
Factory sales
of c a r s show 2, 2„ 72, 2. 75, 3, 3. 4 y e a r c y c l e s and 6. 3 to 6. 5 y e a r
cycles.
Cotton p r i c e s show 2, 5. 91, 6. 3 to 6. 5, 6. 9, 7. 44(89 m o s , ),
7„88, 7 . 9 1 , 7 . 9 5 , 8.42, 9 . 4 7 , 9 . 6 5 , 1 1 . 3 , 12.7 to 1 2 . 9 , 1 4 . 2 7 , 1 7 . 2 5 ,
17.75 and o t h e r s peaking around
2 1 , 42 and 89 y e a r s .
Industrial
stocks show cycle groups a v e r a g i n g 21, 55, and 89 w e e k s , 3, and 3 . 4
years,
42 and 55 m o n t h s , 5 . 9 1 , 5.90,
17.3,
9.0,
9.2,
9. 3 y e a r s , 1 7 . 2 ,
17.7 y e a r s and t h r e e c y c l e s of 18.33 y e a r s in length.
s h a r e p r i c e s show roughly a 34 and 42 month c y c l e .
show a 2 . 0 ,
Sunspot n u m b e r s
5. 91, 8. 7 6, 8. 8, 8. 94, 9. 0 to 9. 3, 11, 1 1 . 5 , 18. 2, 22,
22. 75 and 42 y e a r s .
year,
Copper
Wheat p r i c e s show a 55 lunar month cycle, 5. 96
8, 9.0 to 9 . 3 ,
1 7 . 3 , 34 to 36, 42, 4 2 . 5 , 54, 55 y e a r c y c l e s .
T r e e r i n g s show 5. 91, 5 . 9 3 , 6 . 3 to 6 . 5 , 9. 0 to 9. 3, 1 7 . 7 5 , 1 8 . 2 , 35,
42 and roughly 55 y e a r c y c l e s .
G r e a t Lakes rainfall shows a two y e a r
group, and a l s o a 2 1 , 34, 42 month a v e r a g e group, and a 55, 89 and
144 month c y c l e s .
2.
E a r t h q u a k e s show 17.5 and 35 y e a r c y c l e s .
WHAT RELATIONSHIP I F ANY DO THESE CYCLES
HAVE TO FIBONACCI SEQUENCES?
At f i r s t glance, none.
On c l o s e r examination the 1, 2, 3, 8, 2 1 ,
34, 55, 89 and 144 unit length c y c l e s s p e a k f o r t h e m s e l v e s , but the a p p a r e n t a n o m a l e s of 4 . 5 , 5 . 9 1 , 9, 17~- to 18 and 42 unit length cycles
m u s t be explained.
No s h o r t a g e of r e a s o n a b l e explanations e x i s t s yet
to be s u r e of the right one i m p l i e s m o r e understanding of the u n d e r lying p r i n c i p l e s then we have at the m o m e n t .
1965
FIBONACCI SUMMATION ECONOMICS P A R T II
313
Should t h e s e cycles i n t e r a c t with one another they might s u m m a t e
at t h e i r m e a n .
The 5. 90 to 5. 96 y e a r cycle is roughly 72 months which
is the m e a n between the 55 and 89 month c y c l e s .
The 4. 5 y e a r cycle
is both half of the 9 y e a r cycle and n e a r l y equal to a 55 month c y c l e .
The 5. 91 y e a r cycle is roughly both 1. 618 t i m e s the 42 month cycle
and 0.618 t i m e s the 9* 3 y e a r c y c l e .
I n t e r e s t i n g l y , if the c y c l e s a r e
plotted from the s a m e s t a r t i n g point on a graph in the form of sinusoidal waves it is noted that the 13 and 21 unit and the 34 and 55 unit
cycles will s u m m a t e to z e r o e v e r y 11 j - and 42 units r e s p e c t i v e l y .
A
21 and a 34 unit cycle n e v e r do s u m m a t e to z e r o , w h e r e a s a 21 and a
55 unit cycle will m a x i m i z e at 5. 9 and s u m m a t e to z e r o at 17y u n i t s .
In addition,
the 17+ unit cycle might be half of a 34+ unit c y c l e .
explanation for the 9+ y e a r group is not so s i m p l e .
an 18+ unit cycle,
The
It might be half of
such as that of the s o l a r constant or it might be
double the 55 month or 4y y e a r cycle, or as mentioned above 1. 6 t i m e s
the 5. 91 y e a r c y c l e . Investigation of these a n o m a l e s can b e c o m e c o m plex but s e e m to r e t a i n i n t e r n a l c o n s i s t e n c y .
F o r e x a m p l e t h e r e have
been identified 6, 12 and 13 month cycles in stock p r i c e s .
If t h e s e
w e r e set in motion to s u m m a t e Ave would have
A)
6+13 = 19
B)
19+13 = 32
12+12 = 24
32+19=51
24+12 = 36
51+32 = 83 months
36+24=60 m o n t h s .
Now 83 and 60 months a v e r a g e d together amount to 71-~- m o n t h s , or
5.91 y e a r s .
3.
W H A T OTHER APPARENT COINCIDENCES EXIST THAT
MIGHT BE RELATED TO THE P R O B L E M ?
Wesley Mitchell in his book B u s i n e s s Cycles: The P r o b l e m and
its Setting c a m e to the conclusion after compiling an exhaustive c o r r e l a t i o n of b u s i n e s s cycles with e v e r y conceivable p r o p o s e d c a u s e that
the only phenomenon with which t h e r e is any r e a s o n a b l e c o r r e l a t i o n
is that of s u n s p o t s ,
The s i m i l a r i t y between sunspot cycle length and
the length of a n u m b e r of economic cycles has at the l e a s t called our
attention to the p o s s i b i l i t y of such a r e l a t i o n s h i p being in some way
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FIBONACCI SUMMATION ECONOMICS PART II
Dec.
involved with c e l e s t i a l m e c h a n i c s . If event groupings which a r e cycles
w e r e bunched together by e n e r g y due to planet p o l a r i t y i n t e r a c t i o n it
would not pay to r e j e c t the p o s s i b i l i t y out of hand before the following
was considered,,
Angular m o m e n t u m of a p o l a r i z e d planet rotating
within a s o l a r m a g n e t i c field could like a g e n e r a t o r produce p r e d i c t able amounts of e n e r g y to affect any n u m b e r of f a c t o r s including sunspots and w e a t h e r which c o r r e l a t e well with cycles o b s e r v e d .
Con-
c e r n i n g unit e n e r g y production by r o t a t i o n a l angular m o m e n t u m through
the c e l e s t i a l field it is to be noted that the angular m o m e n t u m involved
in the diurnal e a r t h r o t a t i o n is
5. 9 1 x l 0 4 0 gm, c m ? ,
sec.
the angular m o m e n t u m of the e a r t h moon s y s t e m r o t a t i o n is
34. 4 x l 0 4 0 gm. c m ?
sec.
and that of the e a r t h ' s o r b i t a l motion around the sun is
42. 3 1 x l Q 4 5 g m . c m ? .
seco
T h e r e m a y be exposed now the s t a r t i n g point for an o r d e r l y inv e s t i g a t i o n of a new s y s t e m of quantitative economic p r e d i c t i o n .
The
p u r p o s e in p r e s e n t i n g the information h e r e i n is to e n l i s t the aid of inv e s t i g a t o r s t r a i n e d in a different discipline than the a u t h o r ' s , and it
is felt that the Fibonacci Q u a r t e r l y J o u r n a l is an ideal m e a n s of c o m m u n i c a t i n g with t h e m .
On that account enough m a t e r i a l has been p r e s e n t e d initially to
provide some guidelines c o n c e r n i n g w h e r e solutions m a y lie while for
the m o m e n t r e s t r i c t i n g d e s c r i p t i o n of the a u t h o r ' s a p p r o a c h e s which
might p r e j u d i c e an independent and m o r e s y s t e m a t i c s t a r t b y o t h e r s ,
BIBLIOGRAPHY
6.
M I T C H E L L Wesley C.
Setting,,
National
B u s i n e s s Cycles:
Bureau of E c o n o m i c s
The P r o b l e m and its
R e s e a r c h Inc.
1927.
Seventeenth P r i n t i n g .
7.
CYCLES:
The Official Bulletin of the Foundation for the Study
of Cycles
D e c e m b e r 1963, Vol. 14, No. 12.
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